Cremona's table of elliptic curves

8400 = 2⁴ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	8400j	Isogeny class
Conductor	8400	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-4150656720000000 = -1 · 210 · 32 · 57 · 78	Discriminant
Eigenvalues	2+ 3+ 5+ 7- -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3992,-3099488]	[a1,a2,a3,a4,a6]
j	439608956/259416045	j-invariant
L	1.6400364537715	L(r)(E,1)/r!
Ω	0.20500455672144	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4200k4 33600gu3 25200bs3 1680h4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400j4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	+	-	-4	2	6	-4	8	-2	0	2	10	4	0	-14	-12	-2	-4	0	-2	8	-4	-6	6

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Quadratic twists for elliptic curve 8400j4

-4	8	-3	5	-7
4200k4	33600gu3	25200bs3	1680h4	58800do3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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